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The statistics research group works on applied problems in several areas of statistics from the theoretical, methodological, and computational points of view. Design and analysis of experiments with complex structures are used to help scientists gain higher-quality information from their lab work. Monte Carlo methods inform decisions depending on an unknown future by generating and analyzing myriad plausible scenarios. Algebraic statistics integrates algebra, geometry, and combinatorics into statistical modeling to provide better-fitting models for non-traditional data. Statistical network modeling and uncertainty quantification allow us to detect when certain data structures are more commonly observed than by chance. Bayesian statistics uses prior beliefs to inform statistical inference. We closely collaborate with scientists and engineers from many different disciplines such as mechanical, manufacturing, civil, and transportation engineering, as well as social sciences, biology, neuroscience, business, and management.

Faculty with primary interests in statistics

» M. Cheng » I. Cialenco » F. Hickernell » L. Kang » S. Petrović » D. Stasi

Faculty with secondary interests in statistics

» A. Adler » T.R. Bielecki » R. Ellis » R. Gong

Related seminar

» Algebraic Statistics Seminar

Ph.D. Students

  • Jia He
  • William Schwartz
  • Huiyuan Yu


  • NSF DMS-1522687 (PI F. J. Hickernell and Co-PI G. E. Fasshauer): Stable, Efficient, Adaptive Algorithms for Approximation and Integration, 2015–2018.
  • NSF CMMI-1435902 (PI L. Kang): Collaborative Research: Experimental Design and Analysis of Quantitative-Qualitative Responses in Manufacturing and Biomedical Systems, 2014-2017.
  • AFOSR FA9550-14-1-0141 (PI S. Petrovic): Algebraic Statistics for Network Models, 2014-2017.
  • Fermilab (PI F. J. Hickernell): Modern Monte Carlo Methods for High Energy Event Simulation, Parts I, II, 2015.
  • NSF DMS-1115392 (PI F. J. Hickernell and Co-PI G. E. Fasshauer): Kernel Methods for Numerical Computation, 2011–2014.

Recent Publications

  • Z. Cheng, I. Cialenco, and R. Gong. Bayesian Estimations for Diagonalizable Bilinear SPDEs. Submitted, 2018.
  • X. Huang, L. Kang, M. Kassa, and C. Hall. Two-Stage Functional Data Analysis for Engine Experiments with Quantitative and Qualitative Factors. Submitted. 2017.
  • E. Gross, S. Petrovic, and D. Stasi. The Multiple Roots Phenomenon in Maximum Likelihood Estimation for Factor Analysis. To appear in Advanced Studies in Pure Mathematics, Vol. 75, Mathematical Society of Japan, 2017.
  • N. Kim, D. Wilburne, S. Petrovic, and A. Rinaldo. On the Geometry and Extremal Properties of the Edge-Degeneracy Model. To appear in Proceedings of MNG 2016: The Third SDM Workshop on Mining Networks and Graphs: A Big Data Analytic Challenge, May 7, 2016, Miami, FL, USA, 2017.
  • I. Cialenco. Statistical Inference for SPDEs: an Overview. Statistical Inference for Stochastic Processes (2018), Vol 21, No. 2, pp. 309-329.
  • I. Cialenco, R. Gong, Y. Huang. Trajectory Fitting Estimators for SPDEs Driven by Additive Noise. Statistical Inference for Stochastic Processes (2018), Vol. 21, No. 1, pp. 1-19.
  • T. R. Bielecki, T. Chen, and I. Cialenco. Recursive Construction of Confidence Regions. Electronic Journal of Statistics (2017), Vol. 11, No. 2, pp. 4674-4700.
  • L. Gilquin, Ll. A. Jiménez Rugama, E. Arnaud, F. J. Hickernell, H. Monod, and C. Prieur. Iterative Construction of Replicated Designs Based on Sobol' Sequences. Comptes Rendus Mathematique (2017), Vol. 355, Issue 1, pp. 10–14.
  • E. Gross, S. Petrovic, and D. Stasi. Goodness of Fit for Log-Linear Network Models: Dynamic Markov Bases Using Hypergraphs. Annals of the Institute of Statistical Mathematics (2017), Vol. 69, Issue 3, pp. 673-704.
  • V. Karwa, M. J. Pelsmajer, S. Petrovic, D. Stasi, and D. Wilburne. Statistical Models for Cores Decomposition of an Undirected Random Graph. Electronic Journal of Statistics (2017), Vol. 11, No. 1, pp. 1949-1982.
  • S. Petrovic. A Survey of Discrete Methods in (Algebraic) Statistics for Networks. Algebraic and Geometric Methods in Discrete Mathematics (H. A. Harrington, M. Omar, and M. Wright, eds.), Contemporary Mathematics, Vol. 685, pp. 260-281, American Mathematical Society, 2017.
  • F. J. Hickernell and Ll. A. Jiménez Rugama. Reliable Adaptive Cubature Using Digital Sequences. Monte Carlo and Quasi-Monte Carlo Methods, MCQMC, Leuven, Belgium, April 2014 (R. Cools and D. Nuyens, eds.), Springer Proceedings in Mathematics and Statistics, Vol. 163, pp. 367–383, Springer, 2016.
  • Ll. A. Jiménez Rugama and F. J. Hickernell. Adaptive Multidimensional Integration Based on Rank-1 Lattices. Monte Carlo and Quasi-Monte Carlo Methods, MCQMC, Leuven, Belgium, April 2014 (R. Cools and D. Nuyens, eds.), Springer Proceedings in Mathematics and Statistics, Vol. 163, pp. 407–422, Springer, 2016.
  • L. Kang, J. C. Salgado, and W. A. Brenneman. Comparing the Slack-Variable Mixture Model with Other Alternatives. Technometrics (2016), Vol. 58, No. 2, pp. 255-268.
  • V. Karwa and S. Petrovic. Discussion of “Coauthorship and Citation Networks for Statisticians”. The Annals of Applied Statistics (2016), Vol. 10, No. 4, pp. 1827-1834.
  • I. Cialenco and L. Xu. A Note on Error Estimation for Hypothesis Testing Problems for Some Linear SPDEs. Stochastic Partial Differential Equations: Analysis and Computations (2015), Vol. 2, Issue 3, pp. 408-431.
  • I. Cialenco and L. Xu. Hypothesis Testing for SPDE Driven by Additive Noise. Stochastic Processes and Their Applications(2015), Vol. 125, Issue 3, pp. 819-866.
  • A. B. Slavkovic, X. Zhu, and S. Petrovic. Fibers of Multi-Way Contingency Tables Given Conditionals: Relation to Marginals, Cell Bounds and Markov Bases. Annals of the Institute of Statistical Mathematics (2015), Vol. 67, Issue 4, pp. 621-648.